Hillary Clinton after leaving her daughter’s apartment in New York
Photograph: Brendan Smialowski/AFP/Getty Images

Twenty years ago, almost to the week, Bob Dole, then the Republican nominee for president, slipped and fell off a stage. He was 73, and his aides moved fast to put a positive spin on the tumble: if he can fall down and get right back up again, that proves he’s fit enough for the White House!

But that’s not how most people saw it. Earlier that same day Dole had offered congratulations to the Brooklyn Dodgers, a team that had not existed for four decades. (They became the Los Angeles Dodgers in 1958.) By nightfall TV comedians were renaming the candidate Bob Old. His already ill-starred campaign never recovered.

Eight things that are more important than Hillary's pneumonia

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This is the precedent that will currently be terrifying the Hillary Clinton team, as they watch the endlessly replayed clip of her coming close to collapse, knees buckling as she’s helped into a car following Sunday’s 9/11 memorial events in New York. Veteran Clintonites remember that Dole moment well, for it was Bill Clinton who benefited, comfortably winning re-election less than two months later. Now they fear history is repeating itself – with Hillary on the wrong side.

Are they right to be anxious? Could the image of a frail Hillary Clinton, coupled with the belated admission that she is suffering from pneumonia, prove devastating for her candidacy? Suddenly that is the central question of the 2016 contest – and it touches on far more than the nasty turn the candidate endured on Sunday.

The reasons for Democrats to worry are obvious. For months, with next to no evidence, Donald Trump has been ventilating the claim, long nurtured among rightwing conspiracists, that Clinton has a severe and secret illness.

It’s been a doubly effective strike for Trump. First, by claiming that 68-year-old Clinton lacks “strength and stamina”, or that she “sleeps a lot”, the Republican, who’s 70, has been able to tap into the lingering sexist belief that a woman is too weak to lead. Second, the notion that Clinton has hidden this frailty plays nicely into the view, held by some 60% of the US electorate, that she is dishonest and untrustworthy.

Until Sunday Clinton defenders were able to hit back, dismissing the first line of attack as rank misogyny and the second as unfair exaggeration. But by fainting in view of a camera, and by initially concealing a pneumonia diagnosis that came on Friday, Clinton has allowed Trump to claim vindication. If he has not yet done an “I told you so” tweet, it’s only because he doesn’t have to.

No less damaging are the practical implications. Those who’ve had the illness – including those much younger than Clinton – say that recovery demands total rest and can take seven or eight weeks. She simply does not have that kind of time.

Even if she lightens her campaign schedule, she cannot retreat to her bed between now and 8 November. The first TV debate with Trump, a key moment in any campaign and one that many suspect will determine this race, is just two weeks away. Preparation for that is exacting. What if Clinton forces herself to work, or to do at least a few appearances on the stump, and is visibly unwell again?

All this matters in the US especially because of the particular relationship Americans have with their president. The White House is not quite like, say, 10 Downing Street. Americans are electing not merely a head of government, but also a head of state and national figurehead. There can be an almost primal need to see the president as a protector, the alpha lion strong enough to ensure the safety of the pride.

Of course there have been sick men in the Oval Office: Franklin Roosevelt used a wheelchair, while John F Kennedy had regular steroid injections for excruciating back pain. But both men concealed their frailties from the US public: they knew the voters would struggle to accept weakness in the man they hail as the chief.

Clintonites looking for reassurance can extract a morsel of consolation from the procession of young, fit pundits on the US airwaves sharing their own pneumonia experiences, saying they were knocked sideways by it – but bounced back to full strength.

They’d also note the curious, and surely gender-related, tendency for Hillary to poll better when she has shown vulnerability: her numbers rose when she seemed to shed a tear during her 2008 primary battle against Barack Obama, and, 10 years earlier, when she was the injured party during the Monica Lewinsky scandal.

Those with the rosiest tint to their spectacles would also note that when the media are talking about Clinton’s health, at least they’re not talking about her earlier consignment of half of Trump’s supporters into the “basket of deplorables” as racists, sexists and Islamophobes – a gaffe that meant she was already in trouble even before she crumpled in New York.

There have been sick men in the Oval Office: Roosevelt used a wheelchair, while Kennedy had injections for back pain.

The whole episode, with its focus on both Clinton’s health and honesty, has confirmed again that she is judged by not one but two double standards. The most obvious is gender. Trump’s “strength and stamina” line is just part of a constant and decades-old pattern of faulting aspects of Clinton that would barely be noticed in a man.

Criticised for shouting too loud on the podium or for using her hands too much, or for a thousand other flaws, she said recently that she’s often doing no more than emulating the oratorical style of the men she’s admired. But what we accept in them, too many find unappealing in a woman.

But there’s another double standard that’s costing her dear. Clinton is judged as a politician, held to the standards expected of a serious elected official. Her opponent is not.

It’s undeniable that it has long been the Clinton modus operandi to reveal little, and only when forced. That has fed the impression, for nearly 25 years, that the Clintons are hiding dark and terrible secrets. Once they let in the light, reporters usually find there’s barely anything there: witness the Whitewater “scandal”, talked up as the next Watergate, but which amounted to nothing. Or Clinton’s alleged culpability for the jihadi attack in Benghazi which left the US ambassador and three other Americans dead.

So 60% of Americans think Clinton is dishonest, yet an analysis of her statements showed she was more truthful than every prominent US politician, including Bernie Sanders, bar one: Barack Obama. And now she has promised to release more medical records.

Trump, meanwhile, is such a compulsive liar it’s almost impossible to keep up. (His lies about what he saw on 9/11 could fill a small pamphlet on their own.) Yet somehow this is seen as part of the shtick, part of Trump being Trump – and he’s rarely called on it. So while Clinton was relentlessly grilled during an NBC special last week about her emails, Trump was unchallenged when he breezily claimed that he opposed the Iraq war before it started – even though he’s on tape supporting it.

This is Clinton’s fate, to be doubly judged by double standards. She is a woman and an establishment politician – and now she is ill. Politically, if not medically, her condition is critical.